






def       lowercase__	(					A_:						str  ,      A_:						str		)	->				Optional[Any]:







       """simple docstring"""






       assert x is not None
       assert y is not None

       __UpperCAmelCase     				=len(A_		)
       __UpperCAmelCase     				=len(A_		)

       # declaring the array for storing the dp values
       __UpperCAmelCase     				=[[0] * (n + 1) for _ in range(m + 1		)]  # noqa: E741

       for i in range(1  ,      m + 1		):
              for j in range(1  ,      n + 1		):
                     __UpperCAmelCase     				=1 if x[i - 1] == y[j - 1] else 0

                     __UpperCAmelCase     				=max(l[i - 1][j]  ,      l[i][j - 1]  ,      l[i - 1][j - 1] + match		)

       __UpperCAmelCase     				=""""""
       __UpperCAmelCase				, __UpperCAmelCase     				=m, n
       while i > 0 and j > 0:
              __UpperCAmelCase     				=1 if x[i - 1] == y[j - 1] else 0

              if l[i][j] == l[i - 1][j - 1] + match:
                     if match == 1:
                            __UpperCAmelCase     				=x[i - 1] + seq
                     i -= 1
                     j -= 1
              elif l[i][j] == l[i - 1][j]:
                     i -= 1
              else:
                     j -= 1

       return l[m][n], seq


if __name__ == "__main__":
   __A					=	"AGGTAB"
   __A					=	"GXTXAYB"
   __A					=	4
   __A					=	"GTAB"

   __A				,     __A					=	longest_common_subsequence(a, b)
   print("len =", ln, ", sub-sequence =", subseq)
   import doctest

   doctest.testmod()





_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    8_0_0,
    7_9_9,
    6_0_0,
    5_9_9,
    5_0_0,
    4_0_0,
    3_9_9,
    3_7_7,
    3_5_5,
    3_3_3,
    3_1_1,
    2_8_8,
    2_6_6,
    2_4_4,
    2_2_2,
    2_0_0,
    1_9_9,
    1_7_7,
    1_5_5,
    1_3_3,
    1_1_1,
    8_8,
    6_6,
    4_4,
    2_2,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_7_6,
    9_5_2,
    9_2_8,
    9_0_5,
    8_8_2,
    8_5_8,
    8_5_7,
    8_1_0,
    7_6_2,
    7_1_5,
    7_1_4,
    5_7_2,
    4_2_9,
    4_2_8,
    2_8_6,
    2_8_5,
    2_3_8,
    1_9_0,
    1_4_3,
    1_4_2,
    1_1_8,
    9_5,
    7_1,
    4_7,
    2_4,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_8_8,
    9_7_7,
    9_6_6,
    9_5_5,
    9_4_4,
    9_3_3,
    9_2_2,
    9_1_1,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_5_0,
    3_0_0,
    2_9_9,
    2_6_6,
    2_3_3,
    2_0_0,
    1_9_9,
    1_7_9,
    1_5_9,
    1_4_0,
    1_2_0,
    1_0_0,
    9_9,
    8_8,
    7_7,
    6_6,
    5_5,
    4_4,
    3_3,
    2_2,
    1_1,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_9_5,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_1,
    9_7_8,
    9_7_5,
    9_7_1,
    9_6_7,
    9_6_4,
    9_6_1,
    9_5_7,
    9_5_6,
    9_5_1,
    9_4_7,
    9_4_2,
    9_3_7,
    9_3_3,
    9_2_8,
    9_2_3,
    9_1_9,
    9_1_4,
    9_1_3,
    9_0_8,
    9_0_3,
    8_9_7,
    8_9_2,
    8_8_7,
    8_8_1,
    8_7_6,
    8_7_1,
    8_7_0,
    8_6_4,
    8_5_8,
    8_5_2,
    8_4_6,
    8_4_0,
    8_3_4,
    8_2_8,
    8_2_7,
    8_2_0,
    8_1_3,
    8_0_6,
    7_9_9,
    7_9_2,
    7_8_5,
    7_8_4,
    7_7_7,
    7_7_0,
    7_6_3,
    7_5_6,
    7_4_9,
    7_4_2,
    7_4_1,
    7_3_3,
    7_2_4,
    7_1_6,
    7_0_7,
    6_9_9,
    6_9_8,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_6,
    6_5_5,
    6_4_5,
    6_3_4,
    6_2_3,
    6_1_3,
    6_1_2,
    5_9_8,
    5_8_4,
    5_7_0,
    5_6_9,
    5_5_5,
    5_4_1,
    5_2_7,
    5_2_6,
    5_0_5,
    4_8_4,
    4_8_3,
    4_6_2,
    4_4_0,
    4_3_9,
    3_9_6,
    3_9_5,
    3_5_2,
    3_5_1,
    3_0_8,
    3_0_7,
    2_6_4,
    2_6_3,
    2_2_0,
    2_1_9,
    1_7_6,
    1_3_2,
    8_8,
    4_4,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_9_7,
    9_9_5,
    9_9_2,
    9_9_0,
    9_8_8,
    9_8_6,
    9_8_4,
    9_8_1,
    9_7_9,
    9_7_7,
    9_7_5,
    9_7_2,
    9_7_0,
    9_6_8,
    9_6_6,
    9_6_4,
    9_6_1,
    9_5_9,
    9_5_7,
    9_5_6,
    9_5_4,
    9_5_1,
    9_4_9,
    9_4_6,
    9_4_4,
    9_4_1,
    9_3_9,
    9_3_6,
    9_3_4,
    9_3_1,
    9_2_9,
    9_2_6,
    9_2_4,
    9_2_1,
    9_1_9,
    9_1_6,
    9_1_4,
    9_1_3,
    9_1_0,
    9_0_7,
    9_0_5,
    9_0_2,
    8_9_9,
    8_9_6,
    8_9_3,
    8_9_1,
    8_8_8,
    8_8_5,
    8_8_2,
    8_7_9,
    8_7_7,
    8_7_4,
    8_7_1,
    8_7_0,
    8_6_7,
    8_6_4,
    8_6_1,
    8_5_8,
    8_5_5,
    8_5_2,
    8_4_9,
    8_4_6,
    8_4_3,
    8_4_0,
    8_3_7,
    8_3_4,
    8_3_1,
    8_2_8,
    8_2_7,
    8_2_4,
    8_2_1,
    8_1_7,
    8_1_4,
    8_1_1,
    8_0_8,
    8_0_4,
    8_0_1,
    7_9_8,
    7_9_5,
    7_9_1,
    7_8_8,
    7_8_5,
    7_8_4,
    7_8_0,
    7_7_7,
    7_7_4,
    7_7_0,
    7_6_6,
    7_6_3,
    7_6_0,
    7_5_6,
    7_5_2,
    7_4_9,
    7_4_6,
    7_4_2,
    7_4_1,
    7_3_7,
    7_3_3,
    7_3_0,
    7_2_6,
    7_2_2,
    7_1_8,
    7_1_4,
    7_1_0,
    7_0_7,
    7_0_3,
    6_9_9,
    6_9_8,
    6_9_4,
    6_9_0,
    6_8_5,
    6_8_1,
    6_7_7,
    6_7_3,
    6_6_9,
    6_6_4,
    6_6_0,
    6_5_6,
    6_5_5,
    6_5_0,
    6_4_6,
    6_4_1,
    6_3_6,
    6_3_2,
    6_2_7,
    6_2_2,
    6_1_8,
    6_1_3,
    6_1_2,
    6_0_7,
    6_0_2,
    5_9_6,
    5_9_1,
    5_8_6,
    5_8_0,
    5_7_5,
    5_7_0,
    5_6_9,
    5_6_3,
    5_5_7,
    5_5_1,
    5_4_5,
    5_3_9,
    5_3_3,
    5_2_7,
    5_2_6,
    5_1_9,
    5_1_2,
    5_0_5,
    4_9_8,
    4_9_1,
    4_8_4,
    4_8_3,
    4_7_4,
    4_6_6,
    4_5_7,
    4_4_9,
    4_4_0,
    4_3_9,
    4_2_8,
    4_1_8,
    4_0_7,
    3_9_6,
    3_9_5,
    3_8_1,
    3_6_6,
    3_5_2,
    3_5_1,
    3_3_0,
    3_0_8,
    3_0_7,
    2_8_6,
    2_6_4,
    2_6_3,
    2_4_2,
    2_2_0,
    2_1_9,
    1_7_6,
    1_7_5,
    1_3_2,
    1_3_1,
    8_8,
    4_4,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_9_1,
    9_8_2,
    9_7_4,
    9_6_6,
    9_5_8,
    9_5_0,
    9_4_1,
    9_3_3,
    9_2_5,
    9_1_6,
    9_0_8,
    9_0_0,
    8_9_9,
    8_7_4,
    8_5_0,
    8_2_5,
    8_0_0,
    7_9_9,
    7_0_0,
    6_0_0,
    5_0_0,
    4_0_0,
    3_0_0,
    2_0_0,
    1_0_0,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_9_2,
    9_8_5,
    9_7_8,
    9_7_1,
    9_6_4,
    9_5_7,
    9_4_9,
    9_4_2,
    9_3_5,
    9_2_8,
    9_2_1,
    9_1_4,
    9_0_7,
    9_0_0,
    8_9_9,
    8_7_9,
    8_5_9,
    8_4_0,
    8_2_0,
    8_0_0,
    7_9_9,
    7_6_6,
    7_3_3,
    7_0_0,
    6_9_9,
    6_5_0,
    6_0_0,
    5_9_9,
    5_0_0,
    4_9_9,
    4_0_0,
    3_9_9,
    3_0_0,
    2_9_9,
    2_0_0,
    1_9_9,
    1_0_0,
    9_9,
    0,
]

_SCREAMING_SNAKE_CASE 		=      [
    9_9_9,
    9_9_6,
    9_9_2,
    9_8_9,
    9_8_5,
    9_8_2,
    9_7_9,
    9_7_5,
    9_7_2,
    9_6_8,
    9_6_5,
    9_6_1,
    9_5_8,
    9_5_5,
    9_5_1,
    9_4_8,
    9_4_4,
    9_4_1,
    9_3_8,
    9_3_4,
    9_3_1,
    9_2_7,
    9_2_4,
    9_2_0,
    9_1_7,
    9_1_4,
    9_1_0,
    9_0_7,
    9_0_3,
    9_0_0,
    8_9_9,
    8_9_1,
    8_8_4,
    8_7_6,
    8_6_9,
    8_6_1,
    8_5_3,
    8_4_6,
    8_3_8,
    8_3_0,
    8_2_3,
    8_1_5,
    8_0_8,
    8_0_0,
    7_9_9,
    7_8_8,
    7_7_7,
    7_6_6,
    7_5_5,
    7_4_4,
    7_3_3,
    7_2_2,
    7_1_1,
    7_0_0,
    6_9_9,
    6_8_8,
    6_7_7,
    6_6_6,
    6_5_5,
    6_4_4,
    6_3_3,
    6_2_2,
    6_1_1,
    6_0_0,
    5_9_9,
    5_8_5,
    5_7_1,
    5_5_7,
    5_4_2,
    5_2_8,
    5_1_4,
    5_0_0,
    4_9_9,
    4_8_5,
    4_7_1,
    4_5_7,
    4_4_2,
    4_2_8,
    4_1_4,
    4_0_0,
    3_9_9,
    3_7_9,
    3_5_9,
    3_4_0,
    3_2_0,
    3_0_0,
    2_9_9,
    2_7_9,
    2_5_9,
    2_4_0,
    2_2_0,
    2_0_0,
    1_9_9,
    1_6_6,
    1_3_3,
    1_0_0,
    9_9,
    6_6,
    3_3,
    0,
]
